Computer simulation of thermal convection in Rayleigh-Bénard cell ...

Hubert Jopek
Computer simulation of thermal convection in Rayleigh-Bénard cell
Chapter 3: Description of the geometry in Rayleigh-Bénard model
The Geometry of the Rayleigh-Bénard model is presented below:
Fig. 3.1: The fluid layer model.
the top
The model is a very long narrow fluid layer. There are fixed temperatures at
T
C
and at the bottom
Tw
and the temperature at the bottom is higher so
T
w
> T c
. The difference of the temperature is expressed by the term δT
= T w
−Tc
this is one of the control parameters of the system. Convection appears when the
temperature gradient is big enough, consequently a small packet of fluid starts to
move up into the colder region of higher density. If the buoyant force caused by
difference of density is big enough, then the pocket moves upward so fast that the
temperature cannot drop and the convective flow appears. There is also possible
that the buoyant force is not strong enough, in such a situation the temperature of
the pocket is able to drop before it can move up too much, and as a result fluid stays
stable.
and
Fig. 3.2: Transition from thermal conduction to convective rolls in infinite twodimensional
fluid layer.
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